That would likely force more bailouts, perhaps for countries as large as Spain and Italy, and an even greater slowdown across Europe, which is already teetering on the edge of a recession.

"There is considerable uncertainty surrounding just how severe the impact on the global financial system could be," said Paul Ashworth, chief U.S. economist for Capital Economics. "The exit from the eurozone of one or two of the smallest countries may not be disastrous, but a disorderly break-up of the euro that includes either Spain or Italy could well be."

Here are the top three risks for the United States.

U.S. banks' exposure to sovereign debt: U.S. banks have only about $5.8 billion worth of exposure to Greek debt, a virtually insignificant amount for the banking system as a whole.

But the exposure to other troubled countries in Europe is significantly greater -- more than $50 billion each to Spain and Ireland, $66 billion to Italy and $6.6 billion to Portugal.

But all that doesn't even begin to cover the risks posed to the U.S. banking system if there is a disorderly collapse of the euro, which some say will start with a Greece exit.

"Although U.S. banks have limited exposure to peripheral European countries, their exposures to European banks and to the larger, 'core' countries of Europe are more material," Federal Reserve Chairman Ben Bernanke said in March. "Moreover, European holdings represented 35% of the assets of prime U.S. money market funds in February, and these funds remain structurally vulnerable."

In addition, the real risk to the banking system would be whether financial markets would freeze up as a result of a Greek eurozone default, similar to what happened after the Lehman Brothers bankruptcy in September 2008, which led to a massive credit freeze.

Pullback in U.S. exports: The 17-nation eurozone is the third-largest market for U.S. goods, purchasing $49.2 billion worth in the first quarter of this year, or nearly 13% of overall U.S. exports.

That puts those countries behind only neighboring markets of Canada and Mexico and well ahead of purchases by China or Japan. In fact, the eurozone nations imported more U.S.-produced goods than China and Japan combined.

Jay Bryson, international economist with Wells Fargo Securities, said if Greece and other weaker countries leave the eurozone in the coming months, U.S. exports to all of Europe will take a significant hit.

"When U.S. gross domestic product is growing so slowly, you want every bit of growth you can get," he said.

U.S. businesses slow down: Many products sold by U.S. companies in Europe are made in Europe.

If the value of the euro versus the dollar continues to drop, U.S. goods are going to become more expensive by comparison to those made by European rivals. And that could cut into U.S. business sales and exports around the globe if countries can get cheaper imports from Europe.

Furthermore, if export-driven economies like China see demand from Europe slow, it increases a risk of a so-called "hard landing" for the Chinese economy.

Given the importance of emerging market growth worldwide, a hard landing in China and other export markets poses a significant threat of creating a global recession, according to a report earlier this year from the World Bank.

And the with U.S. GDP of 2.2% in the most recent quarter, it is doubtful the United States can avoid a recession of its own if there is a true global slowdown.